Magnification of a capacitance value has first been discovered as an unwanted side effect of amplification, where the plate-grid capacitance of an electron tube was effectively amplified by the gain of the tube. This phenomenon, called the Miller effect, has thereafter been employed to purposely amplify the value of a capacitance, achieving thereby a large capacitance value with a physically small capacitor. In the integrated analog circuit art, this capability has become quite important because inductors cannot be manufactured economically while small value capacitors can be easily realized. Consequently, analog integrated circuits are manufactured with solely active elements, resistors, and where necessary, small valued capacitors.
Miller effect capacitance magnification occurs when, as shown in FIG. 1, an amplifier (10) having a gain -G has a capacitor (12) connected between the input (15) and output (16) ports of the amplifier. When amplifier 10 of FIG. 1 has a large input impedance, a voltage V applied to port 15 causes a current I to flow between ports 15 and 16, which current flows almost exclusively through capacitor 12 and is, therefore, proportional to the derivative of the voltage across the capacitor. Thus, since the voltage across capacitor 12 is V-(- GV) or (1+ G)V, the current flowing between ports 15 and 16 is EQU i= (1+G)VC (1)
where V is the derivative of V and C is the value of capacitor 12. From equation (1) it may be seen that a pure capacitance appears between ports 15 and 16 and that this capacitance has the value (1+G)C.
The prior art circuit of FIG. 1 has three drawbacks. First, for large capacitance magnification values the gain G must be large, causing the effective capacitance to be highly affected by the gain of the amplifier. Second, in order to obtain a purely capacitive impedance between ports 15 and 16, the amplifier's input impedance must be sufficiently high so as not to shunt an appreciable portion of current away from capacitor 12. Third, because of the high impedance required, it is difficult to develop an amplifier with a large gain value, resulting in a limitation in the attainable capacitance magnification.